tag:blogger.com,1999:blog-9004452969563620551.post6478591251895058895..comments2018-02-08T05:14:43.789+05:30Comments on Paramanand's Math Notes: Theories of Circular Functions: Part 1testernoreply@blogger.comBlogger1125tag:blogger.com,1999:blog-9004452969563620551.post-40115552333713199092016-05-05T12:08:23.101+05:302016-05-05T12:08:23.101+05:30Circular functions actually live naturally on S^1 ...Circular functions actually live naturally on S^1 and not on the reals but in school we only introduce the reals hence the trouble. But I don&#39;t know why we teach it like that in school since we are intuitively aware of at least (and this is enough) two one-dimensional &#39;spaces&#39;: one that extends indefinitely in either &#39;direction&#39; (actually, orientation) and one that returns to the start. In fact, in certain Brahmin cosmologies time was modelled using what we would now think of S^1.<br /><br />But we are lucky that S^1 does have the reals as its <a href="https://en.wikipedia.org/wiki/Covering_space#Universal_covers" rel="nofollow">universal cover.</a><br /><br />Btw, let me say that its great that you have kept your interest in math alive despite working in the industry. Anonymousnoreply@blogger.com